We study a parabolic two-phase system with memory occupying a bounded and smooth domain. The heat exchange at part of the boundary is controlled by a thermostat. Assuming on the phase variable either a relaxation dynamics or a Stefan condition, we prove existence and uniqueness results for feedback control problems corresponding to two different types of thermostat: the relay switch and the Preisach operator. These results are strictly related to the continuous dependence of the solution on the boundary datum, which is investigated in advance.
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S. Gatti, Automatic Control of the Temperature in Phase Change Problems with Memory. Z. Anal. Anwend. 20 (2001), no. 4, pp. 883–914DOI 10.4171/ZAA/1050